Finite numbers of initial ideals in non-Noetherian polynomial rings

D-Bases for Polynomial Ideals over Commutative Noetherian Rings

On annihilator ideals in skew polynomial rings

This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...

Prime Ideals of Finite Height in Polynomial Rings

We investigate the structure of prime ideals of finite height in polynomial extension rings of a commutative unitary ring R. We consider the question of finite generation of such prime ideals. The valuative dimension of prime ideals of R plays an important role in our considerations. If X is an infinite set of indeterminates over R, we prove that every prime ideal of R[X] of finite height is fi...

Noetherian rings without finite normalization

A number of examples and constructions of local Noetherian domains without finite normalization have been exhibited over the last seventy-five years. We discuss some of these examples, as well as the theory behind them.

Grr Obner Bases for Polynomial Ideals over Commutative Noetherian Rings and Related Results ?

We present a completion-like procedure for constructing weak and strong Grr obner bases for polynomial ideals over commutative Noetherian rings with unit. This generalizes all the known algorithms for computing Grr obner bases for polynomial ideals over various diierent coeecient domains. The coeecient domain is incorporated using constraints. Constraints allow us to describe an optimized proce...